The Rotterdammers want Stuivenberg to replace departing coach Arne Slot. Feyenoord have accepted Liverpool's offer to release him from his contract at the end of the season.
AD says Feyenoord are looking towards the Premier League to replace Slot.
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And Stuivenberg is said to be the Dutch club's first choice.
Stuivenberg has earlier in his career been active in various youth teams in Feyenoord. His most recent head coaching assignment was at KRC Genk, which he left in December 2017.